Signals and Systems
Boise State University
Electric Circuits
Electric Circuits
Chalmers
Chalmers
Communications
Systems Group,
Hani
Mehrpouyan,
Signals and Systems,
Communications Systems Group,
Signals and Systems,
Chalmers University of Technology,
Department of
Electrical and Computer Engineering,
Chalmers University
of Technology,
Sweden
Boise State
University
Sweden
c 2010
Lecture 7 (Thevenin’s
Theorem)
c 2010
Sep 28th, 2015
August 20, 2015
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
Boise State c 2015
1
1
1
Signals and Systems
Boise State University
Overview
Circuits
• In this Electric
chapter, the concept
of
superposition will be introduced.
• Source transformation will also be
Chalmers
covered. Communications
Systems Group,
Signals and Systems,
• Thevenin and
Norton’s
theorems will be
Chalmers University of Technology,
covered.
Sweden
c 2010
• Examples of applications for these
August
20, 2015
concepts will be
presented.
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
22 1
Signals and Systems
Boise State University
Source Transformation
Electric Circuits
• It is possible to transform a source from
one form to another
Chalmers
• This can be useful
for simplifying circuits
Communications Systems Group,
• The principle behind
all of these
Signals and Systems,
Chalmers University of Technology,
transformations
is Sweden
equivalence
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
36 1
Boise State c 2015
Signals and Systems
Boise State University
Source Transformation II
Electric Circuits
• A source transformation is the process
of replacing a voltage source vs in series
with a resistor R Chalmers
by a current source is in
Communications Systems Group,
parallel with a resistor
R, or vice versa.
Signals and Systems,
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
47 1
Signals and Systems
Boise State University
Terminal Equivalency
Electric Circuits
• These transformations work because the two
sources have equivalent behavior at their
terminals
Chalmers
• If the sourcesCommunications
are turned
off the resistance at
Systems Group,
the terminals areSignals
bothandRSystems,
Chalmers University of Technology,
• If the terminals are short
Swedencircuited, the currents
need to be the same c 2010
• From this we getAugust
the following
requirement:
20, 2015
vs = is R or is =
Hani Mehrpouyan (hani.mehr@ieee.org)
vs
R
58 1
Boise State c 2015
Signals and Systems
Boise State University
Dependent Sources
Electric Circuits
• Source transformation also applies to
dependent sources
Chalmers
• But, the dependent
variable must be
Communications Systems Group,
handled carefully
Signals and Systems,
Chalmers University of Technology,
• The same relationship
between the
Sweden
voltage and currentc 2010
holds here:
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
69 1
Signals and Systems
Boise State University
Source transformation rules
Electric
Circuits
• Note that
the arrow of
the current source
is directed towards the positive terminal
of the voltage source
Chalmers
• Source transformation
is not possible
Communications Systems Group,
Signals
and Systems,
when R=0 for an
ideal
voltage source
Chalmers University of Technology,
Sweden R≠0
• For a realistic source,
c 2010
• For an ideal current source, R=∞ also
August
2015
prevents the use
of 20,
source
transformation
Hani Mehrpouyan (hani.mehr@ieee.org)
10
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Boise State c 2015
Signals and Systems
Boise State University
Electric Circuits
Chalmers
Communications Systems Group,
Signals and Systems,
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
8
1
Signals and Systems
Boise State University
Electric Circuits
Chalmers
Communications Systems Group,
Signals and Systems,
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
9
1
Signals and Systems
Boise State University
Thevenin’s Theorem
Electric
• In many
circuits, oneCircuits
element will be
variable
• An example of this is household outlet;
Chalmers
many different
appliances may be
Communications Systems Group,
Signals
and Systems,
plugged into the
outlet,
each presenting
Chalmers University of Technology,
a different resistance
Sweden
c 2010
• This variable element
is called the load
2015 to reanalyze
• Ordinarily one August
would20,have
the circuit for each change in the load
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
11
10 1
Signals and Systems
Boise State University
Thevenin’s Theorem II
Electric Circuits
• Thevenin’s theorem states
that a linear two terminal
circuit may be replaced with
a voltage source and
resistor
Chalmers
• The voltage source’s
value Systems Group,
Communications
Signals and Systems,
is equal to the open circuit
Chalmers University of Technology,
voltage at the terminals
Sweden
• The resistance is equal to c 2010
the resistance measured at
the terminals when the
August 20, 2015
independent sources are
turned off.
Hani Mehrpouyan (hani.mehr@ieee.org)
12
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Boise State c 2015
Signals and Systems
Boise State University
Thevenin’s Theorem III
Electric Circuits
• There are two cases to consider when finding
the equivalent resistance
• Case 1: If there areChalmers
no dependent sources,
then the resistance
may
be found by simply
Communications Systems Group,
and Systems,
turning off all theSignals
sources
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
13
12 1
Signals and Systems
Boise State University
Thevenin’s Theorem IV
Electric Circuits
• Case 2: If there are
dependent sources, we
still turn off all the
Chalmers
independent sources.
Communications Systems Group,
Signals and Systems,
v0 (or
• Now apply a voltage
Chalmers University
of Technology,
Sweden
current i0) to the terminals
c 2010
and determine the current
i0 (voltage v0). August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
14
13 1
Boise State c 2015
Signals and Systems
Boise State University
Thevenin’s Theorem V
Electric Circuits
• Thevenin’s theorem is very powerful in
circuit analysis.
• It allows one to simplify
a circuit
Chalmers
• A large circuit
may be
replaced
by a
Communications
Systems
Group,
Signals and Systems,
single independent
voltage
source and a
Chalmers University
of Technology,
Sweden
single resistor.
c 2010
• The equivalent circuit behaves
August
20,same
2015 as the
externally exactly
the
original circuit.
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
15
14 1
Signals and Systems
Boise State University
Negative Resistance?
Electric Circuits
• It is possible for the result of this analysis to
end up with a negative resistance.
• This implies the circuit is supplying power
Chalmers
• This is reasonable with
dependent sources
Communications Systems Group,
• Note that in the
end,
the
Thevenin equivalent
Signals and Systems,
Chalmers
of Technology,
makes working
withUniversity
variable
loads much
Sweden
easier.
c 2010
• Load current can be calculated with a voltage
August 20,
2015
source and two series
resistors
• Load voltages use the voltage divider rule.
Hani Mehrpouyan (hani.mehr@ieee.org)
16
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Boise State c 2015
Signals and Systems
Boise State University
Electric Circuits
Chalmers
Communications Systems Group,
Signals and Systems,
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
16 1
Signals and Systems
Boise State University
Electric Circuits
Chalmers
Communications Systems Group,
Signals and Systems,
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
17 1
Signals and Systems
Boise State University
Electric Circuits
Chalmers
Communications Systems Group,
Signals and Systems,
Chalmers University of Technology,
Sweden
c 2010
August 20, 2015
Hani Mehrpouyan (hani.mehr@ieee.org)
Boise State c 2015
18 1